1. Field of the Invention
The present invention concerns a method for equalizing symbols received from a transmission channel and decoding data therefrom. The invention more specifically concerns an equalization and decoding method which is adaptive to the delay spread of the transmission channel.
2. Description of the Related Art
Equalization is a well known method for removing Inter Symbol Interference (ISI) affecting a transmission channel.
The signal samples at the channel output can be expressed as:                               R          k                =                                            ∑                              i                =                0                                            L                -                1                                      ⁢                                                  ⁢                                          c                i                            ⁢                              D                                  k                  -                  i                                                              +                      η            k                                              (        1        )            
where ci are the channel coefficients defining the impulse response of the transmission channel (CIR), L is the delay spread of the channel, Dk−i is a M-ary modulated symbol and ηk is the sampled additive white Gaussian (AWG) noise affecting the channel. From equation (1) the transmission channel can be viewed as a finite impulse response filter with L taps.
A first class of equalization methods is concerned with symbol-by-symbol equalization. A simple equalization method consists in using a transverse linear filter for cancelling the ISI. Of course, the tap coefficients of the transversal filter can be adapted to track the variations of the channel characteristics. However, linear equalization performs poorly due to the effect of noise enhancement. This effect is mitigated in nonlinear Decision Feedback Equalization (DFE). A decision feedback equalizer comprises two parts: a feedforward part identical to a transverse linear filter and a feedback part including a decision step on the received symbol. The feedback part estimates the ISI contributed by the previously decided symbols and subtracts this estimation from the transverse linear filter output before the decision on the current symbol is made.
A second class of equalization methods derives from a Maximum Likelihood Sequence approach called therefore Maximum Likelihood Sequence Estimation (MLSE). According to this approach, the discrete memory channel is modelled as a finite-state machine, the internal register of which having the length of the channel memory. The most likely transmitted sequence Dk, knowing the received sequence Rk and the channel coefficients, is obtained by the Viterbi algorithm. Since the number of states of the trellis involved in the Viterbi algorithm grows exponentially with the channel memory length, several proposals have been made to reduce the number of states to be taken into account. In a first attempt to mitigate this effect, DDFSE (Delayed Decision Feedback Sequence Estimation) combines MLSE and DFE techniques by truncating the channel memory to a reduced number of terms and by removing in the branch metrics the tail of the ISI using a decision made on the surviving sequence at an earlier step (tentative decision). A further improvement with respect to error propagation, called RSSE, (Reduced State Sequence Estimation) was inspired by an Ungerboeck-like set partitioning principle. The RSSE algorithm was originally disclosed in the article of V. M. Eyuboglu et al. entitled “Reduce-state sequence estimation with set partitioning and decision feedback”, published in IEEE Trans. Commun., Vol. 36, pages 13–20, January 1988. Broadly speaking, in RSSE, the symbols are partitioned into subsets and Viterbi decoding is performed on a subset-trellis, a node or subset-state of the subset-trellis being a vector of subset labels (instead of a vector of symbols like in DDFSE). An advantage of RSSE over DDFSE is that it does not use tentative decisions but embeds the uncertainty of the channel response within the trellis structure.
Another possible way of relaxing the constraints in the decoding trellis is the list-type generalization of the Viterbi algorithm (GVA) proposed by T. Hashimoto in the article entitled “A list-type reduced-constraint generalization of the Viterbi algorithm” published in IEEE Trans. Inform. Theory, vol. IT-33, No 6, November 1987, pages 866–876. The Viterbi algorithm is generalized in the sense that, for a given state in the trellis diagram, a predetermined number S of paths (survivors) leading to that state, instead of a single one in the conventional Viterbi algorithm, are retained at each step. The retained paths are then extended by one branch corresponding to the assumed received symbol and the extended paths are submitted to a selection procedure leaving again S survivors per state. The GVA was applied to equalisation by Hashimoto himself in the above mentioned paper and a list-type Viterbi equalizer and later developed by Kubo et al. the article entitled “A List-output Viterbi equalizer with two kind of metric criteria” published in Proc. IEEE International Conference on Universal Personnal Comm. '98, pages 1209–1213.
Both RSSE and LOVE (List Output Viterbi Equalization) can be regarded as particular cases of Per Survivor Processing (PSP) described in the article of R. Raheli et al. entitled “Per Survivor Processing” and published in Digital Signal Processing, No 3, July 1993, pages 175–187. PSP generally allows joint channel estimation and equalization by incorporating in the Viterbi algorithm a data aided estimation of the channel coefficients. This technique is particularly useful in mobile telecommunication for equalization of fast fading channels.
Recently, a new method of equalisation has been derived from the seminal principle of turbo-decoding discovered by C. Berrou , A. Glavieux, P. Thitimajshima, and set out in the article entitled “Near Shannon limit error-correcting coding and decoding: Turbo-coding”, ICC '93, Vol. 2/3, May 1993, pages 1064–1071. This principle has been successfully applied to equalization by C. Douillard et al. as described in the article entitled “Iterative correction of Intersymbol Interference: Turbo-equalization” published in European Trans. Telecomm., Vol. 6, No 5, September/October 1995, pages 507–511.
The basic principle underlying turbo-equalization is that an ISI channel can be regarded as a convolutional coder and therefore the concatenation of a coder, an interleaver and the transmission channel itself can be considered as equivalent to a turbo-coder.
Turbo-equalization is based on an iterative joint equalization and channel decoding process. FIG. 1 shows an example of a transmission system using turbo-equalization. The transmitter comprises a systematic coder (100), e.g. a sytematic convolutional coder (K,R) where K is constraint length and R is the binary rate, which encodes the input data Ik into error-control coded data Yn, an interleaver (110) outputting interleaved data Yn′ and a M-ary modulator (120), e.g. a BPSK modulator, or a QAM modulator. At the receiving side, the turbo-equalizer TE is represented with dotted lines. The symbols Rn′affected by ISI are supplied to a soft equalizer (140) which outputs soft values Λn′representing the reliability of the estimation of Yn′. The soft equalization may be implemented by a Soft Output Viterbi Algorithm (SOVA) as described in the article of J. Hagenauer and P. Hoeher entitled “A Viterbi algorithm with soft-decision outputs and its applications” published in Proc. IEEE Globecom '89, pages 47.1.1–47.1.7. Alternately the Maximum A Posteriori (MAP) algorithm initially described in the article of L. Bahl, J. Cocke, F. Jelinek and J. Raviv published in IEEE on Information Theory, vol. IT-20, March 1974, pages 284–287 or a variant thereof (e.g. Log MAP, Max Log MAP) can be used. The latter algorithms will be globally referred to in the following as APP-type algorithms since they all provide the a posteriori probability for each bit to be decided. For example, the soft-equalizer of FIG. 1 implements the Log MAP algorithm which conveniently expresses the reliability information in the form of a Log Likelihood ratio Λn′=Λ(Yn′). The soft values Λn′are then de-interleaved by the deinterleaver (150) and supplied to a soft-output decoder which may be here again a SOVA decoder or an APP-type decoder. The soft decoder uses these soft values and the knowledge of the coding algorithm to form soft estimates Λk=Λ(Ik) of the initial data Ik which, in turn, permit to refine the estimation of the received symbols. For this, the latter estimates are passed back to the equalization stage. More precisely, the extrinsic information Extk produced by the decoding stage, i.e. the contribution of that stage to the reliability of the estimation, is obtained by subtracting in (191) the soft-output from the soft-input of the decoder. The extrinsic information Extk is then interleaved in interleaver (180) and fed back as a priori information to the soft equalizer (140). According to the principle of turbo-decoding, the extrinsic information derived from a stage must not be included in the soft input of the same stage. Hence, the extrinsic information Extk is subtracted in (191) from the output of the soft equalizer. The iteration process repeats until the estimation converges or until a time limit is reached. The soft output of the decoder is then compared to a threshold (170) to provide a hard output, i.e. a decision Îk on the bit value.
The reduced state technique has been successfully transposed to the MAP algorithm with the view of applying it to turbo-equalization. In particular, a List-type MAP equalizer is described in unpublished French patent applications FR-A-0000207 and FR-A-0002066 filed by the Applicant on 4.1.2000 and 15.2.2000 respectively and included herein by reference.
The idea of joint channel estimation and equalization has also pervaded turbo-equalization. L. Davis, I. Collings and P. Hoeher have proposed in an article entitled “Joint MAP equalization and channel estimation for frequency-selective fast fading channels” published in Proc. IEEE Globecom '98, pages 53–58, a turboequalizer comprising a MAP equalizer making use of an expanded state trellis. The expansion of the state trellis beyond the channel memory length introduces additional degrees of freedom which are used for estimating the channel parameters. This method is more particularly useful for channels exhibiting fast varying characteristics, for example in the case of a transmission channel involving a high velocity mobile terminal.
Another possible structure of turboequalizer is described in the article of A. Glavieux et al. entitled “Turbo-equalization over a frequency selective channel”, International Symposium on Turbo-codes”, Brest, September 1997. In place of the MAP equalizer illustrated in FIG. 1, the first stage of the turboequalizer comprises a transversal linear filter for cancelling ISI from the received symbols in a decision directed mode followed by a M-ary to binary soft decoder.
Whatever the structure of the turbo-equalizer is, a problem arises in mobile telecommunication when the delay spread in the transmission channel is low or when it operates at low diversity. In such instance, the so-called “turbo-effect”, i.e. the improvement of the estimation reliability over successive iterations, is significantly reduced. This phenomenon, which means that the gain between two consecutive iterations of the iterative process decreases for a given signal to noise ratio Eb/N0 (where Eb is the mean energy received per information bit and N0 the noise bilateral spectral density) can be explained by the fact that turbo-equalization performs better on codes exhibiting large constraint lengths and that the delay spread of a channel can be regarded to some extent as equivalent to the constraint length of a code.